1 Effect of Shock-Induced Cavitation Bubble Collapse on the damage in the Simulated Perineuronal Net of the Brain. Yuan-Ting Wu and Ashfaq Adnan * Mechanical and Aerospace Engineering, the University of Texas at Arlington, Arlington, 76010, USA * [email protected] Appendix 1: Simulation Set-up The detail of our simulation set-up is described in this section. 1. Equilibration: The initial size of the simulation box is 16 nm, 16 nm, and 25 nm containing a total of 599,205 atoms. We have equilibrated the whole system for 60 ps. In the first 10 ps of equilibration, we kept the hyaluronan “fixed” but released this constraint for the next 50 ps of simulation. The equilibration was performed with NPT ensemble (fixed number of atoms, fixed pressure, and fixed temperature) at 300 K and 101 kPa. The temperature and pressure are controlled by using “fix npt” command in LAMMPS 1 . This command performs time integration on Nose-Hoover based equations of motion to generate positions and velocities sampled from the isothermal-isobaric ensemble. More details about the scheme and implementation can be found in LAMMPS website 1 and the linked references therein 2-6 . Specifically, the temperature is controlled by the thermostat that is applied to the translational degrees of freedom for the atoms. The external pressure is controlled by the barostat as scaler hydrostatic pressure. For prescribed values for thermostat and barostat time constants (we used 1 ps for the barostat and 50 fs for the thermostat), the time-averaged temperature and pressure of the atoms attain the target values (i.e 300 K and 101 kPa, respectively). 2. Shock Generation: We have generated shock using “reflective-boundary” method. First, we have replaced the periodic boundaries normal to z-axis to reflecting boundaries. We have generated vacuum between bulk atoms and +z direction (3 nm)/–z direction (7 nm) . We have then subjected the entire box of atoms to a velocity, v p , along positive z-direction. The applied velocity v p causes the entire box of atoms propel towards and eventually impact the reflective boundary at the same velocity v p . Such impact on the reflecting boundary induces a shock wave on the impacting atoms. It is evident
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Effect of Shock-Induced Cavitation Bubble Collapse on thedamageintheSimulatedPerineuronalNetoftheBrain.Yuan-TingWuandAshfaqAdnan*
MechanicalandAerospaceEngineering,theUniversityofTexasatArlington,Arlington,76010,USA*[email protected]:SimulationSet-upThedetailofoursimulationset-upisdescribedinthissection.
1. Equilibration:Theinitialsizeofthesimulationboxis16nm,16nm,and25nmcontainingatotalof599,205atoms.We
haveequilibratedthewholesystemfor60ps. In the first10psofequilibration,wekept thehyaluronan“fixed”but
releasedthisconstraint for thenext50psofsimulation.TheequilibrationwasperformedwithNPTensemble (fixed
numberof atoms, fixedpressure, and fixed temperature) at 300K and101 kPa. The temperature andpressure are
controlledbyusing“fixnpt”commandinLAMMPS1.ThiscommandperformstimeintegrationonNose-Hooverbased
equationsofmotiontogeneratepositionsandvelocitiessampledfromtheisothermal-isobaricensemble.Moredetails
about the scheme and implementation can be found in LAMMPS website1 and the linked references therein2-6.
Specifically,thetemperatureiscontrolledbythethermostatthatisappliedtothetranslationaldegreesoffreedomfor
theatoms.Theexternalpressureiscontrolledbythebarostatasscalerhydrostaticpressure.Forprescribedvaluesfor
thermostatandbarostattimeconstants(weused1psforthebarostatand50fsforthethermostat),thetime-averaged
temperatureandpressureoftheatomsattainthetargetvalues(i.e300Kand101kPa,respectively).
2. ShockGeneration:Wehavegeneratedshockusing“reflective-boundary”method.First,wehavereplacedtheperiodic
boundariesnormaltoz-axistoreflectingboundaries.Wehavegeneratedvacuumbetweenbulkatomsand+zdirection
(3nm)/–zdirection(7nm).Wehavethensubjectedtheentireboxofatomstoavelocity,vp,alongpositivez-direction.
Theappliedvelocityvpcausestheentireboxofatomspropeltowardsandeventuallyimpactthereflectiveboundaryat
thesamevelocityvp.Suchimpactonthereflectingboundaryinducesashockwaveontheimpactingatoms.Itisevident
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frompriorliteraturesthatthephysicsofshockwaveformedbyreflectionissameasconventionalpiston-drivenshock
waveformation.Theshockvelocitygeneratedbyoursystemagreeswithexperimentalresultsandothersimulationwork.
Appendix2:CavitationFormationandNucleationSiteIn this section,we have investigated the distance between cavitation-induced bubble and hyaluronan to determine the
minimumdistanceatwhichhyaluronanexhibitstableconfiguration.Thesimulationboxcontainingwater,hyaluronan,and
ionsareslowlystretchedupto23%involume,whichenablesnanocavitationtoform.
Thissetofsimulationisaimedtoobtainthecharacteristicdistancebetweennanobubbleandhyaluronan(FigureA1).The
initialsizeofthesimulationboxis16nm,16nm,and25nmcontainingatotalof599,205atomswitha12foldhyaluronan
(~500atoms),whichisthesameequilibratedboxinthemainarticle.Westretchedtheentiresimulateddomain,includingall
oftheatoms,for10.78%involume(3.47%inlength)within10ps.Thenwecontinuuedthesimulationforanother40pswith
fixeddoaminsize.Duringtheentiresimulation,thetemperatureisfixedat300Kwiththedampingconstantof12.5fs.
FigureA1shows the results. It canbeobserved thatwhen thebox started to stretch,pressure starts togodownbelow
atmospheric(i.e.,buildingupofnegativepressureortensilepressure).Oncethenegativepressureisreachedthecritical
pressureforbubblenucleation(inourcaseitis~-170MPa,whichisclosetotheexperimentalresultfrom7),bubblesstart
toform,andthepressurestopstobuildfurtherevenwhentheboxiscontinuedtoexpand.Aftertheboxstopstretching(10
ps),thepressurestarttoriseup.Itcanalsobeobservedthatthenear-sphericalbubblesareformedfrommanynucleation
sites.Mostbubbles,withanaveragesizeof~2nm,areseentonucleateabout~3-5nmawayfromthehyaluronan-liquid
interface.Thenearestbubblenucleationsitewecapturedhasthedistance~0.5nmfrombubblesurfacetothehyaluronan.
Attheendofthesimulation(50ps),allthecavitation-bubbletendedtomergeintoone,whichisthelowestenergystateat
givenconstraint.
Byobservingthe interactionbetweenthenewlynucleatedbubbleandhyaluronan, it isclearthathydrophilichyaluronan
tendstorepelthebubbleaway.Thebubblesareonlystableataminimumdistanceof0.5nmfromthehyaluronanimplying
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thepresenceofatleastoneortwolayersofwaterbetweenthebubblesurfaceandthehyaluronan.Theminimumdistance
of0.5nmislaterusedinthemainarticle.
Appendix3:Visualcomparisonofthethreesetsofsimulation(withrotatedHAasinitialcondition)InFig.A2,resultsofallthreesetsofsimulationshavebeenshown.ThethresholdofHAbreakingarethesameinallthree
sets.SincetheHAofthethreesetsarerotatedby90degreeseach,thebrokensegmentoftheHAareatdifferentlocation
butfollowingthesamepatternofbreakingglyosidicbondandbreakingglucosestructure(mostlyfor7.2km/scases).
References1 http://lammps.sandia.gov/doc/fix_nh.html(lastaccessedon5-15-2017)2 Plimpton,S.Fastparallelalgorithmsforshort-rangemoleculardynamics.Journalofcomputationalphysics117,1-
19,doi:10.1006/jcph.1995.1039(1995).
3 Shinoda,W.,Shiga,M.&Mikami,M.Rapidestimationofelasticconstantsbymoleculardynamicssimulationunderconstantstress.PhysicalReviewB69,134103,doi:10.1103/PhysRevB.69.134103(2004).
4 Martyna,G.J.,Tobias,D.J.&Klein,M.L.Constantpressuremoleculardynamicsalgorithms.TheJournalofChemicalPhysics101,4177-4189,doi:10.1063/1.467468(1994).
5 Parrinello,M.&Rahman,A.Polymorphictransitionsinsinglecrystals:Anewmoleculardynamicsmethod.Journal
ofappliedphysics52,7182-7190,doi:10.1063/1.328693(1981).6 Tuckerman, M. E., Alejandre, J., López-Rendón, R., Jochim, A. L. & Martyna, G. J. A Liouville-operator derived
measure-preservingintegratorformoleculardynamicssimulationsintheisothermal–isobaricensemble.JournalofPhysicsA:MathematicalandGeneral39,5629,doi:10.1088/0305-4470/39/19/S18(2006).
7 Azouzi,M.E.M.,Ramboz,C.,Lenain,J.-F.&Caupin,F.Acoherentpictureofwateratextremenegativepressure.
NaturePhysics9,38-41,doi:10.1038/nphys2475(2013).
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0 10 20 30 40 50-200
-150
-100
-50
0
50
Cel
l pre
ssur
e (M
Pa)
Time (ps)
c
FigureA1.(a,b)Cavitation-inducedbubbleformationandcoalescence.Allwateratomsexceptthoseonthebubblesurfacehavebeenremovedforclarity.Theblueshadesrepresentbubblesurface.(c)Accumulatedpressureinthesimulationcell.
t=22ps t=50ps
a b
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FigureA2.AtomisticsimulationsnapshotsshowingevolutionofHAimpactedbyWHjet,basedonresultsfromsimulationset(a)one(b)twoand(c)three.
a b c
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